We introduce Interference Feedback Computing (IFC), a universal computational paradigm that achieves state- ful, adaptive computation through recursive regulation of wave interference patterns. Unlike conventional digital processors that store state in bistable memory elements, IFC systems embed memory directly within the phase space of interfering waves—whether optical, quantum, or acoustic. We establish the theoretical foundations of IFC through fixed-point analysis, stability conditions, and convergence guarantees, proving that IFC systems can approximate arbitrary iterative solvers while operating at the physical timescales of wave propagation. Experi- mental validation spans three distinct physical implemen- tations: (i) photonic processors using Mach-Zehnder in- terferometers achieving constraint satisfaction for 16,266- variable problems in 26.36s, (ii) quantum processors on trapped-ion hardware (Quantinuum H2, Rigetti Ankaa- 3) demonstrating sub-2% forecast error on temporal se- quences, and (iii) classical wave simulators converging to 10−10 residual accuracy on nonlinear root-finding. These results establish IFC as a foundational framework for next-generation analog computing, with implications for energy-efficient AI acceleration, real-time optimization, and the development of wave-based general intelligence architectures.